Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23758008 | C2 | semidirect |
| 2. #23757980 | C2 | semidirect |
| 3. #23757629 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757572 | C2 | semidirect |
| 6. #23757568 | C2 | semidirect |
| 7. #23757490 | C2 | semidirect |
| 9. C8×Dic314 | C2 | semidirect |
| 10. #23757353 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 122. C157 | #3361 | semidirect |
| 133. C4×SD16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757980 | 2 |
| #23757629 | 2 |
| #23757620 | 2 |
| #23757572 | 2 |
| #23757568 | 2 |
| #23757490 | 2 |
| #23757468 | 2 |
| C8×Dic314 | 2 |
| #23757353 | 2 |
| C4×SD16×C157 | 2 |
| #3361 | 157 |